An ANOVA test yields a non-significant F-statistic. What does this suggest about the group means?

An ANOVA test yields a non-significant F-statistic. What does this suggest about the group means?

• A. All group means are equal
• B. There is at least one difference among means
• C. There is no evidence of differences among group means after accounting for variability
• D. The model is misspecified

Answer: (C)

In ANOVA, you’re comparing how much of the total variation comes from differences between group means versus variation within each group. The F statistic measures that ratio. If the F statistic is not significant, you don’t have evidence that the group means differ beyond what would be expected by random variability within groups. In plain terms, after accounting for variability, there isn’t detectable evidence of differences among the means. This doesn’t prove the means are exactly equal—it could be that true differences exist but are too small or the study lacks power to detect them. It also doesn’t imply the model is misspecified.

In ANOVA, you’re comparing how much of the total variation comes from differences between group means versus variation within each group. The F statistic measures that ratio. If the F statistic is not significant, you don’t have evidence that the group means differ beyond what would be expected by random variability within groups. In plain terms, after accounting for variability, there isn’t detectable evidence of differences among the means. This doesn’t prove the means are exactly equal—it could be that true differences exist but are too small or the study lacks power to detect them. It also doesn’t imply the model is misspecified.